KZ-MO 2000 Problem 8

Given a triangle $ABC$ and a point $M$ inside it. Prove that $\min \{MA, MB, MC\} + MA + MB + MC <AB + BC + AC.$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.